Algebra 12 - Binary Relations

The lecture introduces the concept of binary relations, explaining how ordered pairs can represent relationships between elements of two sets. It uses examples with sets A and B, comparing binary relations to Cartesian products. The lecture also discusses binary relations within a single set and visual representations in the XY plane, highlighting that binary relations are subsets of Cartesian products.

What is a binary relation in the context of sets?

• A relation that involves only one set

• A relation that involves two sets

• A relation that involves three sets

• A relation that involves no sets

What is the significance of ordered pairs in binary relations?

• They only exist in the Cartesian product

• They are unrelated to binary relations

• They define the relationship between elements of two sets

• They can be swapped without changing the relation

How is the set L different from the Cartesian product of sets A and B?

• L is unrelated to the Cartesian product

• L is larger than the Cartesian product

• L is a subset of the Cartesian product

• L contains all possible ordered pairs

What happens to relation L if no one in set A likes any fruit in set B?

• L becomes the Cartesian product

• L remains unchanged

• L becomes an empty set

• L becomes larger than the Cartesian product

What does the relation T represent in the context of set A?

• A relation of height comparison

• A relation of equality

• A relation between different sets

• A relation of preference

What does the Cartesian product of a set with itself represent?

• A set with all possible ordered pairs

• A set with no ordered pairs

• A set with unordered pairs

• A set with only one ordered pair

How is a point on the XY plane related to binary relations?

• It represents a single set

• It represents a binary relation with infinite pairs

• It represents an ordered pair of real numbers

• It represents a binary relation with no pairs